# Limits, Series, and Fractional Part Integrals

## Problems in Mathematical Analysis

• OvidiuĀ Furdui
Book

Part of the Problem Books in Mathematics book series (PBM)

1. Front Matter
Pages i-xviii
2. Ovidiu Furdui
Pages 1-97
3. Ovidiu Furdui
Pages 99-137
4. Ovidiu Furdui
Pages 139-251
5. Back Matter
Pages 253-274

### Introduction

Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving real analysis problems. The book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works on topics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types.

Most problems are neither easy nor standard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having these problems collected in the book is to stimulate the creativity and the discovery of new and original methods for proving known results and establishing new ones.

The book is divided into three parts, each of them containing a chapter dealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals; the second chapter deals with the calculation of special classes of integrals involving a fractional part term; and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a numerical or a functional term.

### Keywords

Riemann-Zeta numbers fractional part integrals real analysis problems special constants special limits

#### Authors and affiliations

• OvidiuĀ Furdui
• 1
1. 1., Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4614-6762-5
• Copyright Information Springer Science+Business Media New York 2013
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics
• Print ISBN 978-1-4614-6761-8
• Online ISBN 978-1-4614-6762-5
• Series Print ISSN 0941-3502